Abstract

A procedure for the selective extinction of the scattered light based on “null ellipsometry” [R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977)] is presented. The technique allows scattering measurement from individual layers of a multilayer component by extinguishing the scattered light from the other layer interfaces. The technique is easily applicable to multilayer components with nearly identical surface profiles at every interface and little significant bulk scattering. Anal ysis is provided to determine the conditions required to extinguish the light from the excluded interfaces isolating the scattered light from the desired interface. An analysis of sensitivity of the extinction conditions to experimental parameters and to layer optical thickness is also provided. Experimental data collected using the technique are compared with measurements made using a white-light optical surface profilometry.

© 2011 Optical Society of America

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References

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  1. J. M. Elson, J. P. Rahn, and J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
    [CrossRef] [PubMed]
  2. A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061(1977).
    [CrossRef]
  3. A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171(2002).
    [CrossRef] [PubMed]
  4. C. Amra, C. Grezes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]
  5. G. Mie, “Optics of turbid media,” Ann. Phys. 330, 377–445(1908).
    [CrossRef]
  6. J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219(1983).
    [CrossRef] [PubMed]
  7. T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
    [CrossRef]
  8. S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. G. Georges, C. Deumié, and C. Amra, “Selective probing and imaging in random media based on the elimination of polarized scattering,” Opt. Express 15, 9804–9816 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. T. A. Germer, “Polarized light scattering by microroughness and small defects in dielectric layers,” J. Opt. Soc. Am. A 18, 1279–1288 (2001).
    [CrossRef]
  14. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  15. P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).
  17. C. Amra, D. Torricini, and P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
    [CrossRef] [PubMed]
  18. C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
    [CrossRef]

2007 (1)

2005 (2)

2002 (1)

2001 (2)

T. A. Germer, “Characterizing interfacial roughness by light scattering ellipsometry,” AIP Conf. Proc. 550, 186–190(2001).
[CrossRef]

T. A. Germer, “Polarized light scattering by microroughness and small defects in dielectric layers,” J. Opt. Soc. Am. A 18, 1279–1288 (2001).
[CrossRef]

1997 (1)

1996 (1)

1993 (2)

1991 (1)

P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

1983 (1)

1980 (1)

1977 (1)

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061(1977).
[CrossRef]

1908 (1)

G. Mie, “Optics of turbid media,” Ann. Phys. 330, 377–445(1908).
[CrossRef]

Albrand, G.

Amra, C.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bennett, J. M.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Bruel, L.

Bussemer, P.

P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Deumié, C.

Dumas, P.

Duparré, A.

Elson, J. M.

Ferre-Borrull, J.

Georges, G.

Germer, T. A.

Gilbert, O.

Gliech, S.

Grezes-Besset, C.

Ishimaru, A.

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061(1977).
[CrossRef]

Kassam, S.

P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Kehl, K.

P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Maure, S.

Mie, G.

G. Mie, “Optics of turbid media,” Ann. Phys. 330, 377–445(1908).
[CrossRef]

Notni, G.

Rahn, J. P.

Richier, R.

Roche, P.

Steinert, J.

Torricini, D.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

AIP Conf. Proc. (1)

T. A. Germer, “Characterizing interfacial roughness by light scattering ellipsometry,” AIP Conf. Proc. 550, 186–190(2001).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Optics of turbid media,” Ann. Phys. 330, 377–445(1908).
[CrossRef]

Appl. Opt. (8)

J. M. Elson, J. P. Rahn, and J. M. Bennett, “Relationship of the total integrated scattering from multilayer-coated optics to angle of incidence, polarization, correlation length, and roughness cross-correlation properties,” Appl. Opt. 22, 3207–3219(1983).
[CrossRef] [PubMed]

T. A. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[CrossRef]

S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35, 5573–5582 (1996).
[CrossRef] [PubMed]

J. M. Elson, J. P. Rahn, and J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980).
[CrossRef] [PubMed]

A. Duparré, J. Ferre-Borrull, S. Gliech, G. Notni, J. Steinert, and J. M. Bennett, “Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components,” Appl. Opt. 41, 154–171(2002).
[CrossRef] [PubMed]

C. Amra, C. Grezes-Besset, and L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

C. Amra, D. Torricini, and P. Roche, “Multiwavelength (0.45–10.6 μm) angle-resolved scatterometer or how to extend the optical window,” Appl. Opt. 32, 5462–5474 (1993).
[CrossRef] [PubMed]

C. Deumié, R. Richier, P. Dumas, and C. Amra, “Multiscale roughness in optical multilayers: atomic force microscopy and light scattering,” Appl. Opt. 35, 5583–5594 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Proc. IEEE (1)

A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proc. IEEE 65, 1030–1061(1977).
[CrossRef]

Waves Random Media (1)

P. Bussemer, K. Kehl, and S. Kassam, “Theory of light scattering from rough surfaces and interfaces and from volume inhomogeneities in an optical layer stack,” Waves Random Media 1, 207–221 (1991).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Figures (13)

Fig. 1
Fig. 1

Experimental setup: a retardation plate and an analyzer are placed in front of the scattered field detector.

Fig. 2
Fig. 2

(a) Scattering by the totality of an optical component and (b) scattering from one interface when the scattered light from the others is extinguished.

Fig. 3
Fig. 3

(a) Total scattering, (b) extinction of the interface 0 scattering, and (c) extinction of the interface 1 scattering.

Fig. 4
Fig. 4

Extinction conditions [(a) phase shift and (b) analyzer angle] for an H single layer.

Fig. 5
Fig. 5

Scattered intensity before and after extinction of each H single layer interface. The incidence angle equals 67 ° .

Fig. 6
Fig. 6

Extinction conditions [(a) phase shift and (b) analyzer angle] for a 2H2L2H multilayer, in order to select interface 0, interface 1, interface 2, or interface 3.

Fig. 7
Fig. 7

Scattered intensity before and after extinction of each 2H2L2H multilayer interface. The incidence angle equals 67 ° .

Fig. 8
Fig. 8

Sensitivity with (a) η and (b) ψ variations: scattered intensity before and after extinction of a glass substrate in the case of errors in the (a) phase shift value and in (b) analyzer angle value.

Fig. 9
Fig. 9

Variations of the extinction conditions [(a) phase shift and (b) analyzer angle] with the layer optical thickness.

Fig. 10
Fig. 10

Variations of the scattered intensity with layer optical thickness.

Fig. 11
Fig. 11

Profiles measured by optical profilometry of (a) substrate and (b)  coating.

Fig. 12
Fig. 12

Scattered intensity before extinction and after extinction of one of the interfaces.

Fig. 13
Fig. 13

Roughness spectra of interfaces (a) 0 and (b) 1 deduced from selective extinction and profilometry measurements.

Equations (22)

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A ( θ , ϕ ) = A s ( θ , ϕ ) + A p ( θ , ϕ ) ,
f ( A ( θ , ϕ ) ) = cos ψ A s ( θ , ϕ ) + sin ψ e i η A p ( θ , ϕ ) ,
f ( A ( θ , ϕ ) ) = cos ψ ( A s ( θ , ϕ ) + z A p ( θ , ϕ ) ) ,
z = tan ψ e i η ,
f ( A ( θ , ϕ ) ) = 0 z = tan ψ ( θ , ϕ ) e i η ( θ , ϕ ) = A s ( θ , ϕ ) A p ( θ , ϕ ) .
ψ ( θ , ϕ ) = arctan | A s ( θ , ϕ ) A p ( θ , ϕ ) | , η ( θ , ϕ ) = π + arg ( A s ( θ , ϕ ) A p ( θ , ϕ ) ) .
A ( θ , ϕ ) = i A i ( θ , ϕ ) + A * ( θ , ϕ ) .
f ( A ) = cos ψ ( A s + z A p ) = cos ψ ( i A i s + A s * + z ( i A i p + A p * ) ) .
z i k = i k A s i i k A p i .
A u v ( θ , ϕ ) = i c u v i ( θ , ϕ ) g i ( θ , ϕ ) A u .
g i ( θ , ϕ ) = g ( θ , ϕ ) .
A u v ( θ , ϕ ) = g ( θ , ϕ ) i c u v i ( θ , ϕ ) A u .
ψ = arctan | i c s i ( θ , ϕ ) i c p i ( θ , ϕ ) | , η = π + arg ( i c s i ( θ , ϕ ) i c p i ( θ , ϕ ) ) .
A u v ( θ , ϕ ) = c u v 0 ( θ , ϕ ) g ( θ , ϕ ) A u + c u v 1 ( θ , ϕ ) g ( θ , ϕ ) A u .
cos ψ 0 ( A s 0 + z 0 A p 0 ) = 0.
f ( A ) = cos ψ 0 [ ( A s 0 + A s 1 ) + z 0 ( A p 0 + A p 1 ) ] = cos ψ 0 [ ( A s 0 + z 0 A p 0 ) + ( A s 1 + z 0 A p 1 ) ] .
f ( A ) = cos ψ 0 [ A s 1 + z 0 A p 1 ] = f ( z 0 , A 1 ) .
f ( A ) = cos ψ 0 ( A s + z 0 A p ) .
γ ( θ , ϕ ) = 4 π 2 S | g ( θ , ϕ ) | 2 ,
f ( A ) = cos ψ 0 [ A s 1 + z 0 A p 1 ] = cos ψ 0 [ ( c s 1 g 1 A s ) + z 0 ( c p 1 g 1 A p ) ] = g 1 cos ψ 0 [ ( c s 1 A s ) + z 0 ( c p 1 A p ) ] ,
A s = A p .
f ( A ) = g 1 cos ψ 0 [ c s 1 + z 0 c p 1 ] A = g 1 [ c s 1 + c p 1 ] A .

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